A closely related question is that of the boundedness of resolvent operators. A foundational paper in this direction is due to Kenig, Ruiz and Sogge [1]}, who considered this question for second order, constant coefficient operators on the Euclidean space. Their results were later improved by Gutiérrez [2]} in the case of the Laplacian. The case of general compact manifolds was also considered, see in particular Dos Santos Ferreira-Kenig-Salo [3]} and Bourgain-Shao-Sogge-Yao [4]}.
